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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Tangent bundles to regular basic sets in hyperbolic dynamics


Author: Luchezar Stoyanov
Journal: Proc. Amer. Math. Soc. 140 (2012), 1623-1631
MSC (2010): Primary 37D20, 37D40
Published electronically: August 18, 2011
MathSciNet review: 2869147
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Abstract: Given a locally maximal compact invariant hyperbolic set $ \Lambda$ for a $ C^2$ flow or diffeomorphism on a Riemann manifold with $ C^1$ stable laminations, we construct an invariant continuous bundle of tangent vectors to local unstable manifolds that locally approximates $ \Lambda$ in a certain way.


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Additional Information

Luchezar Stoyanov
Affiliation: School of Mathematics, University of Western Australia, Crawley, WA 6009, Australia
Email: stoyanov@maths.uwa.edu.au

DOI: http://dx.doi.org/10.1090/S0002-9939-2011-11001-3
PII: S 0002-9939(2011)11001-3
Received by editor(s): July 28, 2010
Received by editor(s) in revised form: November 27, 2010, and January 10, 2011
Published electronically: August 18, 2011
Additional Notes: The author thanks the referee for useful comments and suggestions.
Communicated by: Bryna Kra
Article copyright: © Copyright 2011 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.